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Magnetohydrodynamics natural convection and entropy generation in a hybrid nanofluid complex enclosure considering finned-heater

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Abstract

The current study investigates the influence of MHD on the natural heat transfer considering the irreversibility in a complex-shaped cavity with the existence of inner roundish heater with four attached fins utilizing finite element formulation. Three different cases are considered to figure out the major characteristics of temperature, stream function and total generated entropy, Nusselt number in addition to Bejan number. Concentrated attention is directed to the enclosure geometry modifications and the varied length of attached fins and their impacts. The parameters of study are ranged as follows; Rayleigh number \(\left({10}^{3}\le \mathrm{Ra}\le {10}^{6}\right)\), Hartmann number \(\left(0\le \mathrm{Ha}\le 60\right)\), fins’ length \(\left(0.1\le H\le 0.3\right)\). The novelty of the present work is on studying all of these parameters in the complex enclosure considering three different cases of the shape of the outer walls so that the star-shaped enclosure is classified as case 1. With increasing the length that separated between the outer arc of the star enclosure, the octagonal-shaped enclosure will appear as denoted in case 2 and 3. It had been seen that at low Rayleigh number \(\left(\mathrm{Ra}={10}^{4}\right)\), case one is the best choice in heat transfer bettering while it is the lowest case at high Rayleigh number \(\left(\mathrm{Ra}={10}^{6}\right)\). Additionally, the influence of Hartmann number on the total entropy generation reduction percentage for case three is \(63.57\%\) while it is 51.11% for case two while Hartmann number had negligible impact of entropy generation reduction for case one. Lastly, the highest Bejan number is at fin length \(\left(H=0.3\right)\) is recorded for case one.

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Abbreviations

B :

Magnetic field

C p :

Specific heat at constant pressure (kJ kg−1 K−1)

g :

Gravitational acceleration (m s−2)

k :

Thermal conductivity (W m−1 K−1)

P :

Dimensionless pressure

Pr:

Prandtl number (νf/αf)

H :

Length of heater (m)

R o :

Base circle (m)

Ra:

Rayleigh number

Ha:

Hartmann number

T :

Temperature (K)

T c :

Temperature of the cold surface (K)

T h :

Temperature of the hot surface (K)

S :

Dimensional Entropy Generation

\({\overline{S} }_{\mathrm{gen}}\) :

Dimensionless Entropy Generation

Be:

Bejan Number

\(\mathrm{Nu}\) :

Average Nusselt number hot inner circular cylinder

U :

Dimensionless velocity component in x-direction

u :

Velocity component in x-direction (m s−1)

V :

Dimensionless velocity component in y-direction

v :

Velocity component in y-direction (m s−1)

X :

Dimensionless coordinate in horizontal direction

x :

Cartesian coordinates in horizontal direction (m)

Y :

Dimensionless coordinate in vertical direction

y :

Cartesian coordinate in vertical direction (m)

α :

Thermal diffusivity (m2 s−1)

θ :

Dimensionless temperature (T−Tc/ΔT)

\({\rm K}\) :

Thermal Conductivity (W m−1·K)

\(\psi\) :

Dimensional stream function (m2 s−1)

Φ:

Angle of circular cylinder

\(\Psi\) :

Dimensionless stream function

\(\sigma\) :

Electrical conductivity

Gr:

Grashof number

Μ :

Dynamic viscosity (kg m−1 s−1)

Ν :

Kinematic viscosity (m2 s−1)

Β :

Volumetric coefficient of thermal expansion (K−1)

Ρ :

Density (kg m−3)

c:

Cold

f:

Fluid (pure)

h:

Hot

hnf:

Hybrid nanofluid

Min:

Minimum

Amp.:

Amplitude (m)

Max:

Maximum

n :

Number of corrugations

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under Grant Number RGP. 2/7/44

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Authors and Affiliations

  1. Mechanical Engineering Department, University of Al-Qadisiyah, Al-Qadisiyah, 58001, Iraq

    Ammar Abdulkadhim, Naseer H. Hamza & Khaled Al-Farhany

  2. Mechanical Engineering Department, College of Engineering, Babylon University, Babylon, Iraq

    Hameed K. Hamzah, Farooq H. Ali & Isam Mejbel Abed

  3. Department of Physics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia

    Nejla Mahjoub Said

  4. Air Conditioning and Refrigeration Techniques Engineering Department, College of Engineering and Technologies, Al-Mustaqbal University, Babylon, 51001, Iraq

    Azher M. Abed

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  1. Ammar Abdulkadhim
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  4. Khaled Al-Farhany
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Abdulkadhim, A., Hamzah, H.K., Hamza, N.H. et al. Magnetohydrodynamics natural convection and entropy generation in a hybrid nanofluid complex enclosure considering finned-heater. J Therm Anal Calorim 149, 1535–1563 (2024). https://doi.org/10.1007/s10973-023-12732-x

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